Question 155529
Solve for x:
{{{Log(x)+Log(2x) = 10}}} Apply the "product rule" for logarithms.{{{Log(a)+Log(b) = Log(a*b)}}}
{{{Log(x*(2x)) = 10}}} Simplify the left side.
{{{Log(2x^2) = 10}}} Apply the power rule for logarithms. {{{Log(a^n) = n*Log(a)}}}
{{{2*Log(2x) = 10}}} Divide both sides by 2.
{{{Log(2x) = 5}}} Convert to the equivalent exponential form:{{{Log[b](x) = y}}}--->{{{b^y = x}}}, so...
{{{10^5 = 2x}}}
{{{100000= 2x}}} Divide both sides by 2.
{{{highlight(x = 50000)}}}